// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/QR>

template<typename Derived1, typename Derived2>
bool
areNotApprox(const MatrixBase<Derived1>& m1,
			 const MatrixBase<Derived2>& m2,
			 typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision())
{
	return !((m1 - m2).cwiseAbs2().maxCoeff() <
			 epsilon * epsilon * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));
}

template<typename MatrixType>
void
product(const MatrixType& m)
{
	/* this test covers the following files:
	   Identity.h Product.h
	*/
	typedef typename MatrixType::Scalar Scalar;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
	typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
	typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
	typedef Matrix<Scalar,
				   MatrixType::RowsAtCompileTime,
				   MatrixType::ColsAtCompileTime,
				   MatrixType::Flags & RowMajorBit ? ColMajor : RowMajor>
		OtherMajorMatrixType;

	Index rows = m.rows();
	Index cols = m.cols();

	// this test relies a lot on Random.h, and there's not much more that we can do
	// to test it, hence I consider that we will have tested Random.h
	MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols);
	RowSquareMatrixType identity = RowSquareMatrixType::Identity(rows, rows),
						square = RowSquareMatrixType::Random(rows, rows), res = RowSquareMatrixType::Random(rows, rows);
	ColSquareMatrixType square2 = ColSquareMatrixType::Random(cols, cols),
						res2 = ColSquareMatrixType::Random(cols, cols);
	RowVectorType v1 = RowVectorType::Random(rows);
	ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
	OtherMajorMatrixType tm1 = m1;

	Scalar s1 = internal::random<Scalar>();

	Index r = internal::random<Index>(0, rows - 1), c = internal::random<Index>(0, cols - 1),
		  c2 = internal::random<Index>(0, cols - 1);

	// begin testing Product.h: only associativity for now
	// (we use Transpose.h but this doesn't count as a test for it)
	VERIFY_IS_APPROX((m1 * m1.transpose()) * m2, m1 * (m1.transpose() * m2));
	m3 = m1;
	m3 *= m1.transpose() * m2;
	VERIFY_IS_APPROX(m3, m1 * (m1.transpose() * m2));
	VERIFY_IS_APPROX(m3, m1 * (m1.transpose() * m2));

	// continue testing Product.h: distributivity
	VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);
	VERIFY_IS_APPROX(square * (m1 - m2), square * m1 - square * m2);

	// continue testing Product.h: compatibility with ScalarMultiple.h
	VERIFY_IS_APPROX(s1 * (square * m1), (s1 * square) * m1);
	VERIFY_IS_APPROX(s1 * (square * m1), square * (m1 * s1));

	// test Product.h together with Identity.h
	VERIFY_IS_APPROX(v1, identity * v1);
	VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
	// again, test operator() to check const-qualification
	VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r, c), static_cast<Scalar>(r == c));

	if (rows != cols)
		VERIFY_RAISES_ASSERT(m3 = m1 * m1);

	// test the previous tests were not screwed up because operator* returns 0
	// (we use the more accurate default epsilon)
	if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
		VERIFY(areNotApprox(m1.transpose() * m2, m2.transpose() * m1));
	}

	// test optimized operator+= path
	res = square;
	res.noalias() += m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
	if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
		VERIFY(areNotApprox(res, square + m2 * m1.transpose()));
	}
	vcres = vc2;
	vcres.noalias() += m1.transpose() * v1;
	VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);

	// test optimized operator-= path
	res = square;
	res.noalias() -= m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
	if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
		VERIFY(areNotApprox(res, square - m2 * m1.transpose()));
	}
	vcres = vc2;
	vcres.noalias() -= m1.transpose() * v1;
	VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);

	// test scaled products
	res = square;
	res.noalias() = s1 * m1 * m2.transpose();
	VERIFY_IS_APPROX(res, ((s1 * m1).eval() * m2.transpose()));
	res = square;
	res.noalias() += s1 * m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square + ((s1 * m1).eval() * m2.transpose()));
	res = square;
	res.noalias() -= s1 * m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square - ((s1 * m1).eval() * m2.transpose()));

	// test d ?= a+b*c rules
	res.noalias() = square + m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
	res.noalias() += square + m1 * m2.transpose();
	VERIFY_IS_APPROX(res, 2 * (square + m1 * m2.transpose()));
	res.noalias() -= square + m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square + m1 * m2.transpose());

	// test d ?= a-b*c rules
	res.noalias() = square - m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
	res.noalias() += square - m1 * m2.transpose();
	VERIFY_IS_APPROX(res, 2 * (square - m1 * m2.transpose()));
	res.noalias() -= square - m1 * m2.transpose();
	VERIFY_IS_APPROX(res, square - m1 * m2.transpose());

	tm1 = m1;
	VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
	VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);

	// test submatrix and matrix/vector product
	for (int i = 0; i < rows; ++i)
		res.row(i) = m1.row(i) * m2.transpose();
	VERIFY_IS_APPROX(res, m1 * m2.transpose());
	// the other way round:
	for (int i = 0; i < rows; ++i)
		res.col(i) = m1 * m2.transpose().col(i);
	VERIFY_IS_APPROX(res, m1 * m2.transpose());

	res2 = square2;
	res2.noalias() += m1.transpose() * m2;
	VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
	if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
		VERIFY(areNotApprox(res2, square2 + m2.transpose() * m1));
	}

	VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r),
					 (square.adjoint() * square.col(r)).eval());
	VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());

	// vector at runtime (see bug 1166)
	{
		RowSquareMatrixType ref(square);
		ColSquareMatrixType ref2(square2);
		ref = res = square;
		VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.col(0).transpose() * square.transpose(),
						 (ref.row(0) = m1.col(0).transpose() * square.transpose()));
		VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.block(0, 0, rows, 1).transpose() * square.transpose(),
						 (ref.row(0) = m1.col(0).transpose() * square.transpose()));
		VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.col(0).transpose() * square,
						 (ref.row(0) = m1.col(0).transpose() * square));
		VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.block(0, 0, rows, 1).transpose() * square,
						 (ref.row(0) = m1.col(0).transpose() * square));
		ref2 = res2 = square2;
		VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.row(0) * square2.transpose(),
						 (ref2.row(0) = m1.row(0) * square2.transpose()));
		VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.block(0, 0, 1, cols) * square2.transpose(),
						 (ref2.row(0) = m1.row(0) * square2.transpose()));
		VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.row(0) * square2,
						 (ref2.row(0) = m1.row(0) * square2));
		VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.block(0, 0, 1, cols) * square2,
						 (ref2.row(0) = m1.row(0) * square2));
	}

	// vector.block() (see bug 1283)
	{
		RowVectorType w1(rows);
		VERIFY_IS_APPROX(square * v1.block(0, 0, rows, 1), square * v1);
		VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0, 0, rows, 1), square * v1);
		VERIFY_IS_APPROX(w1.block(0, 0, rows, 1).noalias() = square * v1.block(0, 0, rows, 1), square * v1);

		Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> w2(cols);
		VERIFY_IS_APPROX(vc2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.noalias() = vc2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = vc2.block(0, 0, cols, 1).transpose() * square2,
						 vc2.transpose() * square2);

		vc2 = square2.block(0, 0, 1, cols).transpose();
		VERIFY_IS_APPROX(square2.block(0, 0, 1, cols) * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.noalias() = square2.block(0, 0, 1, cols) * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = square2.block(0, 0, 1, cols) * square2,
						 vc2.transpose() * square2);

		vc2 = square2.block(0, 0, cols, 1);
		VERIFY_IS_APPROX(square2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.noalias() = square2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
		VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = square2.block(0, 0, cols, 1).transpose() * square2,
						 vc2.transpose() * square2);
	}

	// inner product
	{
		Scalar x = square2.row(c) * square2.col(c2);
		VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
	}

	// outer product
	{
		VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
		VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(),
						 m1.block(r, 0, 1, cols).transpose() * m1.block(0, c, rows, 1).transpose());
		VERIFY_IS_APPROX(m1.block(0, c, rows, 1) * m1.row(r), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
		VERIFY_IS_APPROX(m1.col(c) * m1.block(r, 0, 1, cols), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
		VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0, 0, rows, 1) * m1.block(r, 0, 1, cols));
		VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0, c, rows, 1) * m1.block(0, 0, 1, cols));
	}

	// Aliasing
	{
		ColVectorType x(cols);
		x.setRandom();
		ColVectorType z(x);
		ColVectorType y(cols);
		y.setZero();
		ColSquareMatrixType A(cols, cols);
		A.setRandom();
		// CwiseBinaryOp
		VERIFY_IS_APPROX(x = y + A * x, A * z);
		x = z;
		VERIFY_IS_APPROX(x = y - A * x, A * (-z));
		x = z;
		// CwiseUnaryOp
		VERIFY_IS_APPROX(x = Scalar(1.) * (A * x), A * z);
	}

	// regression for blas_trais
	{
		VERIFY_IS_APPROX(square * (square * square).transpose(), square * square.transpose() * square.transpose());
		VERIFY_IS_APPROX(square * (-(square * square)), -square * square * square);
		VERIFY_IS_APPROX(square * (s1 * (square * square)), s1 * square * square * square);
		VERIFY_IS_APPROX(square * (square * square).conjugate(), square * square.conjugate() * square.conjugate());
	}

	// destination with a non-default inner-stride
	// see bug 1741
	if (!MatrixType::IsRowMajor) {
		typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
		MatrixX buffer(2 * rows, 2 * rows);
		Map<RowSquareMatrixType, 0, Stride<Dynamic, 2>> map1(
			buffer.data(), rows, rows, Stride<Dynamic, 2>(2 * rows, 2));
		buffer.setZero();
		VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
		buffer.setZero();
		VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
		buffer.setZero();
		VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
	}
}
